Modelling of interaction of relativistic and nonrelativistic flows on adaptive grids

We consider some numerical aspects of the mathematical modeling of composite flows (relativistic and non-relativistic) on adaptive computational grids applied to a double system "pulsar–optical star". The pulsar is the source of ultra-relativistic wind of electron-positron plasma and the optical star is the source of the non-relativistic wind. In the domains of relativistic and non-relativistic flows, the plasma dynamics is described by various systems of equations. Moreover, the wind parameters are such that their modeling in a homogeneous way faces significant difficulties. Despite the fact that the distance between the partners of the binary system varies depending on the orbital phase, the flow is a self-similar one and is determined by the dimensionless parameters of the problem. The flow pattern can vary significantly with the variation of these parameters. This fact requires the flexibility of the algorithm for constructing of a grid which is adaptive to the solution. In this work we present some possibilities to use the adaptive grids for modeling of the above mentioned class of composite flows.